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IMO 2012 NO 2

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Misalkan $n \geq 3$ suatu bilangan bulat, dan misalkan $a_2$, $a_3$, $a_4$, ... , $a_n$ adalah bilangan real positif sehingga $\displaystyle\prod\limits_{i=2}^n a_i = 1$. Buktikan bahwa


$\displaystyle\prod\limits_{i=2}^n (1+a_i)^i > n^n$

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